Calculating apparatus



Dec- 15, 19 J. Y. P. R. ROSENOER ETAL 3,161,762

CALCULATING APPARATUS Filed Sept. 8, 1961 4 Sheets-Sheet 1 In ve nlors JACQUES XP. R. RGSENGM RAYMOND f. AJ'PRAIVGER) Dec. 15, 1964 J. Y. P. R. ROSENOER ETAL 3,

' CALCULATING APPARATUS 7 Filed Sept. 8. 1961 4 Sheets-Sheet 2 I n venlors JACQUES X f. R. RDSEIVOER RA YMOIVA E. ASPRA NGERS tto ne Dec. 15, 1964 J. Y. P. R. ROSENOER ETAL 3,161,762

CALCULATING APPARATUS 4 Sheets-Sheet 5 Filed Sept. 8. 1961 L L L .L L L .L L L S R o ON I. M A 9 R my M U\| R P I. w Y 5 m 0 a h k @I Q A A N D b u q 0 Q Q a.. has

Dec. 15, 1964 J. Y. PJR. ROSENOER ETAL 3,161,762

CALCULATING APPARATUS Filed Sept. 8, 1961 4 Sheets-Sheet 4 FIG 5 Inventors .mcquss mmnosavom RAY"? 0 58. B

United States Patent The invention relates to a calculating apparatus for computing a linear digital function of the various digits a forming a number, said function involving multiplication of each digit by a factor associated to the rank of the digit, and addition of the resultant products. The said linear function is able to assume any one of p dilferent digital values from zero to p1, Where p is a predeterminedinteger, and where the value of the function is computed modulo p by means of a binary counter, i.e. by taking the least non-negative residues after dividing by p. The said calculating apparatus is particularly adapted to provide a proof operation in which manifestations of certain sets of symbols, e.g. certain decimal numbers, are checked for accuracy, such that for an accurate manifestation of any such certain set the various symbolsforming the set invariably produce the same final proof-condition; i.e;-the same value for said linear functiomwhile for an inaccurate manifestation a different proof condition is obtained. i

Such a calculating apparatus is already known from the unit delivering the coded information and the calculating 3 apparatus which is required to operate in a serialmannei'.

Also, for the known apparatus, the factors associated to the various ranks must be determined byv a mechanism which makes one step as each digit is fed. Moreover, the

number of different factors is limited tothe number of stages of the binary counter. 3 i

It is an object of the present invention to provide calculating apparatus which readily permits verification of binary codedinformation, so that this calculatingap paIatusmay be directly fed from a memory unit wherein the information is registered in coded form. f

Another objectof the invention is to avoid rank ascertaining means in order todetermine the factor corresponding to the rank." a The'calculating apparatus according to the present invention is characterized by the fact that said digital function is computed by an iterative process, each new function F being obtained by first adding'a, to theprevious function F taking the sum as the least non-negative residue with respectto p, thereafter multiplying this sum residue by 2, and taking the productas the least nonnegative residue with respectto p. The apparatus is further characterized in that it includes feeding means for feeding each of said digitsto saidbinary counter under the form of sets of binary bits according to. aconstant weight binary code, each of'the weights being a power or 2; in such a manner that the binary bits constituting each digit are respectively applied to the bistable devices ofj, cori'esponding weight in the 'counter thus 'executijng the adding operation, and that it includes ldoubling means for' bringing 'thereafter each of "said bistable devices'into a 3,161,762 Patented Dec. 15, 1964 predetermined condition, to execute the multiplication operation.

It is to be noted that a. calculating apparatus for computing a digital function by an iterative process is already-known per se, eg from the Belgian Patent 591,979 (N. Rouche). But the apparatus according to the present invention provides a particularly simple arrangement for proving binary coded digits.

A further object of the invention is to prove digits modulowll or 13 without complicating the operation of a 4-stage binary counter. According to a further characteristic of the invention said binary counter comprises four intercoupled bistable the input of the first and third (or second) bistable devices so that, when said one output is activated, the states of said first and third bistable devices are reversed.

'-Yet a further object of the invention is to feed the binary coded digits serially bit by bit to the binary counter without lengthening the time required to carry out the multiplication operation. a V

The invention is further characterized by the fact that saidconstant'weight binary code is the 2421 code, e.g. Aiken code, that it includes a fifth bistable device, serving as a memory device, and a timing arrangement for providing four distinct time intervals t to t that the first bit of each of said digits is fed by said feeding means to said fifth bistable device during time interval t whereas the'second and fourth bits ofeach of said digits are fed to said third and first bistable devices, during time intervals t ..and t respectively, that when the first bit is a 0 the third bit is fed, during the tiineinterval i to said second bistable device via second gating means conditioned by the 0-output of said fifth bistable device, that when the first bit is a 1 the third bit is fed, during the timeinterval to said second or third bistable devices when it is a 0 or a 1 respectively and via third and fourth gating means which are conditioned by the l-output of said fifth bistable device, and that said doubling means apply, during the time interval .13 a doubling pulse to all the O-o'utputs of said lowing description of embodiments taken in conjunction with the accompanying drawings wherein: FIGS. 1,2-and 3 represent the calculating apparatus according to the invention; Y

FIG. 4 gives pulse wave forms for the apparatus of a FIGURES 1, 2", 3..

.FIG. 5 shows another embodiment of the, calculating apparatus according tothe invention.

The calculating apparatus'will particularly be described for calculating the abovementioned:function, the'diiferent digitsa a, being fed to it under form ofthe Aiken or 2-4+2l code. This code form may for instance be obtained from. al coder network operated from digit keys pushed by an operator. i

- The calculating apparatus principally includes a four stage binary counter comprising four bistable devices BS to B8 each functioning -as a scale-of-two counter which delivers its l-output a pulse to the following stage when it is triggered back into its O-Coridition.

The four binary bitsof each decimal digit a, respectively have the weights 2, 4, Z'and 1 and since the weights of the ,second, third, second and first stages of the counter respectively diiring't'our distinct time intervals 1 t t and 3 which are controlled by a timing arrangement disissed below.

It should be remarked that all bistable and rnonostable :vices used in the present calculating apparatus are norally in their O-condition i.e. with their O-output activated 1d their state may only be reversed when a negative volt- ;e step is applied to their input.

The timing arrangement includes an] astable multivifator AS (FIG. 3') which continuously produces'atrits ltput leads land 2 a first and second series of pulses in hich each pulse has a width equal to half of the basic ming period (66 11.8.), the pulsesin the two series being t phase opposition with the respect to each other. The rst and second pulse series are respectively applied to the [put leads of monostable devices M8 and MS (FIG. which are each triggered to their unstable condition for .8 s. by the negative edge of each pulse applied therei. The 6.8 ,as. pulses at the outputs of monostable delces M8 and MS are respectively called A and B ulses.

When theoperator pushes a digit key a coder network not shown) is operated which delivers at its four output :ads the four binary bits of the Aiken'code of the keyed igit. These four bits are applied to the input leads 1 of re coincidence gates G 6 ,65 and G (FIG. 1) respecvely and also to the input leads 1 to 4 of the OR-gate 1 The input 5 of OR-gate M 3 is' activated when the igit keyed is a 0, so that the output'of this OR-gate is ontinuousl'y activated upon operation of any digit key.

Due to this the input leads 1 of the coincidence gates i and G (FIG. 3) are respectively activated anddectivated and since the input lead 2 of the gate G is oincidentally activated; by the O-output of the bistable ,evice B8 an A pulse is passed viathis gate G to the -input of the bistable device B5 which is thus triggered its l-condition by the trailing edge of this A pulse. Jpon deactivation of the 0 output, on output lead p of vistable device B8 the monostable device M8 is )IOllght to its unstable condition for 120 as. Simulaneously the input ,2 of the coincidence, gate G is detctivated, preventing further transfer of signals therehrough.

Due to the l-outputof the bistable device 'BS being ictviated the input 3 of the coincidence gate G is acivated so that the A pulses,rfollowing the one which rigge'red the bistable device B are passed through his gate G Due to the output. of the monostable device M5 being .ctivated for 120 ,uS. the output lot the OR-gate M 5 activated, this output being initially inactive since the nput leads 2, 3 and 4 of the OR-gate are respectively :onnected-to the initially deactivated l-outputs of the bitable devices B8 to B8 (FIG. 2), the latter being inerconnected to form an 8-state binary counter. It is iowever to be remarked that if any one of the bistable levices BS 4 is in its l-condition, the output of the )R-gate M is activated so that in fact the 120 4s. pulse lelivered by the monostable device M8 only constitutes t pulse forrstarting the operation. Indeed, as soon as he output of the gate M is activated, B pulses arefed hrough the gate, G to the different coincidence gates 3 to G which'form part ofthe counter BS 45.

The first of these B pulses triggers bistable. device B8 0 its l-condition via the gate G since the input 2 of this gate is conditioned by the normally activated O-output )f the bistable device B5 The second B pulse triggers :he bistable device B8 back to its O-condition via the gate G since the input 2 of this gate is activated, and

also triggers the bistable device BS into its l-condition via the gate G blsin'ce the input leads 2 and 3 of this gate are both activated. The third B pulse again triggers the bistable device.BS intoits l condition etc. The different states of the bistable devices BS are shown in FIG. .4. i

. The input l'of thejgate G being activated the A pulses may be fed through this gate on the one hand via the inverter 12 to the OR-gate M (lead 0) and onthe other hand to the input leads 3 of the gates G to G (lead b) and to the l-input of the bistable device BS which is thus trtiggered to its l-condition by the trailing edge of the first A pulse applied thereto. The. bistable device BS being in its l-condition the input 2 of the gate G is deactivated so that no A pulses may be fed through this gate to the bistable device BS Since the input 1 of the OR-gate M is conditioned by the O-output (lead 0) of the bistable device B5 of the counter BS it is clear that this input 1 will be activated as long as the bistable device B8 remainsin the O-condition i.e. until the fourth B pulse is applied to the counter BS This means that the output (on. lead h) of the OR-gate M will remain continuously activated during the entire time interval in which the first three inverted A pulses appearing at the output of the inverter 1,; are applied to the input 2 of OR-gate M and that only fourth and following inverted A pulses appearing at the.

output of the inverter I control the output of the OR- gate M As can be seen on the drawings the inputs 2 of AND gates G to G are also conditioned in common by the above mentioned O-output of the bistable device B8 (lead c) so that only the first three A pulses appearing at the output of AND gate G (lead b) will pass through these gates. The use of three such A pulses represents asafety measure, as will become clear from what follows. As mentioned above the four binary bits constituting a digit are respectively applied to the inputs 1 of AND gates G G G and G Thuswhen the keyed information applied is a 1 the corresponding AND-gate input 1 is activated so that the first arriving A-pulse is able to trigger the corresponding bistable devices BS BS BS and ES, to their l-condition via the gates G G G G respectively. However, if any 1 information pulse applied to an input 1 is not suitablyshaped, during the'timeof occurrence of the first A pulse, due to contact vibrations of the corresponding digit key, the pulse appearing at the output of the corresponding gate G G G G may not trigger the corresponding bistable deviceto its l-condition. Such vibrations generally appear at the start of the key pushing and they are in general damped before the second A pulse arrives so that the second A pulse is then able to trigger the corresponding bistable device.

Afther the appropriate ones of the bistable devices BS have been set to their l-eondition by.binary 1 signals applied to their associated AND-gates, in cooperation with the first or second A pulse applied thereto, each of the set devices activates an input 1 of a corresponding one of the gate G associated to the next following bistable device BS which is then triggered to its 1- condition bythe second or third A, pulse. Consequently the input 1 of the OR-gate M the input 1 of the OR-gate M the input 40f the OR-gate M and the inputs of the OR-gate M are respectively deactivated when the first, second, third and fourth bits of the binary representation of the decimal digit fed to the counter are, respectively, 1.

The signal on input leads 1, 2 and 3' of the OR gate M define the above time interval t the signals on input leads 2, 3 and 4 of the OR-gate M define the above time interval t the signals on the input leads 1, 2, 3 of the OR-gate M define the above time interval t and finally the signals on input leads 2, 3 and 4 of the OR-gate M define theti'me interval t Indeed, considering first the OR-gate M t'he input leads 2, 3 and 4 are respectively connectedjvia the leads c, e and g to the O-output of the bistable device B8 and the l-outputs of the bistable de- Supp'osing thatthe first bit of the decimal digit fed to 5 the counter is a l the input 1 of the OR-gat'e M is thus deactivated so that the fourth inverted A pulse appearing at the output of the inverter I; (lead is then able to control the output of the OR-gate M In the same manner it may be shown that when the second, third and fourth bits of a digit fed to the calculating apparatus are l, the fifth, sixth and seventh inverted A pulses appearing at the output of the inverter I Will'control the output of the OR-gates M M and M respectively during the time intervals t t and 1.; respectively. I

When the counter constituted by the bistable devices B8 to B8 is in its sixth position, the inputs 1, 2 and 3 of the gate G are activated so that the next following or seventh B pulse is fed through gate G to the input of the monostable device M8 which is thus triggered to its unstable condition by the trailing edge of the seventh B pulse. In this manner the output of the OR-gate M is activated for 220 microseconds so that due to the input 2 of the gate G being also activated by the same 220 microsecond pulse via the OR-gate M12, the B pulses at input 2 of OR-gate 11, are unable to affect the output of gate G The trailing edge of the 220 microsecond pulse which thus appears at the output of the gate G resets bistable devices BS to BS to their 0-condi tions and sets the monostable device M8 to its unstable condition for 6.8 microseconds. The same trailing edge also triggers the bistable device B5 back to its O-condition, so that the input 1 of the gate G is deactivated thus preventing further passage of A pulses to leads b and 0. It is to be remarked that the above trailing edge is produced after the counter BS has been reset to its zero state.

Summarizing, the function of the timing arrangement constituted by the counter BS is to control the production of pulses at the outputs of the OR-gates M M M and M during time intervals t t t and t respec tively and to produce after the counter BS has been reset to its zero position, a pulse for trigggering the bistable devices BS and the monostable device M8 to their O-condition and unstable condition respectively.

The main element of the calculating apparatus is a binary counter which comprises the bistable devices ES -B8 each acting as a scale-of-two counter.

The common input of the bistable device B8,, is connected to the output of the coincidence gate G the input leads 1 and 2 of which are respectively conditioned by the normally activated output leads of the OR-gates M and M respectively. The l-output of bistable device BS is connected to the normally deactivated input of the monostable device MS the normally deactivated output of which is coupled to the normally deactivated input of the monostable device MS Y The common input of the bistable device BS is connected to the output of the OR-gate M the input leads 1 and 2 of which are connected to the output leads of the coincidence gates G and G respectively. The input leads 1 and 2 of the coincidence gate G are conditioned by the normally activated output of OR-gate M and the normally activated O-output of the monostable device MS respectively, whereas the input leads 1 and 2 of the coincidence gate G are connected to the normally activated output leads of the OR-gates M and M respectively.

The coincidence gate G and the monostable devices M5 and M5 associated to the bistable device BS correspond to the coincidence gate G and the monostable devices M8 and MS; associated to the bistable device B8 The input leads 1 and 2 of the coincidence gate G are connected to the normally activated output leads of the OR-gates M and M; respectively.-

The l-output of the bistable device B8 is coupled to the common input of the bistable deviceBS via the monostable devices M8 and M5 Since the counter B55 includes four bistable devices it is able to assume 16 states but as it is the function of the calculating apparatus to count mod p wherein p=l1 it is necessary to suppress 5 of the 16 possible states of the counter.

Therefore the last stage (B8 of the counter is coupled to the first (BS and third (B8 stages thereof in the following manner. The normally activated O-output of the bistable device B8 is coupled (via lead 1') to the normally deactivated input of the monostable device M8 and the normally deactivated output of monostable device MS, is connected to the normally deactivated input of the monostable device M8 The normally activated O-output of the monostable device M8 is, as mentioned above, coupled via the OR-gate M and lead i to the coincidence gates G and G associated to the bistable devices BS and BS respectively. The other input 2 of the above OR-gate M is conditioned by the normally deactivated l-output of the monostable device As will become clear from what follows it is sometimes necessary to suppress 6 of the 16 possible positions of the counter B8 Therefore the normally last stage (B312) of the counter is coupled to the second (B5 and third (B8 stages thereof in the following manner. The deactivated l-output (lead R) of the bistable device B8 is connected to the input 1 of the gate G the other input 2 of which is conditioned by the normally deactivated output of the monostable device M8 The output of this gate G is connected to the normally deactivated input of the monostable device M8 the normally deactivated output of which is coupled to the normally deactivated input of the monostable device MS The normally activated 0-output of monostable device M8 is connected via the OR-gate M (lead 1) to the input leads 1 of the above mentioned gates G and G associated to the bistable devices B8 and B8 respectively. The other input 2 of the OR-gate M is also conditioned by the output of the monostable device M8 The normally deactivated output of the monostable device M8 is further connected to the normallydeactivated input of the monostable dew'ee MS the normally activated 0-output of which is connected (via lead m) to the O-inputs of the bistable devices B5 The calculation of the function wherein a a a are the diiterent digits of -a number, will now be described in detail. It will be appreciated that for certain keyed combinations of decimal digits (a the calculated value of the function will be zero (mod 11), and this may be taken as a proof condition indicative of accurate keyings, or, in general, manifestations, of: such combinations. Thus, if all input numbers to be selected or keyed-for example, all account num bers in a bookkeeping systembelong to the set of all. such certain combinations, the selections are easily verified by this apparatus. For example the number 123 will be proved, so that the following operations have to be made [(1 2)+2]2+3 i.e. first the first digit 1 is multiplied by 2, then the seconddigit 2 is added to this product (2), then the resultant sum (4) is multiplied by 2 and finally the third digit 3 is added to the second product (8). Thus the sum, decimal 11, should be obtained or since mod 11, or, in general, mod p of this sum is to be taken, the final result should be the proof condition zero. 2

Therefore the first decimaldigit l, or 0001 in Aiken code, is fed to the calculating apparatus i.e. during the time intervals t t t and t the bits 0, 0, 0, l are fed to the input'leadscl of the gates 6 G G G respectively. Hence only the .bistable device BS will be triggered to its l-eondition during the time interval t via the gate G Since the weights of the bistable devices BS are 2, 2 2 and 2 respectively, as 1 is registered in the counter.

By the negative trailing edge of the 220 ,uS. pulse ape aring at the output of the gate G g'the monostable levice M5 is triggeredto its unstable condition. Due this the monostable device "M is also triggered to ts unstable condition and the 3.3 s. or so called doubling iulse appearing at its O-output' is applied to the-O-inputs )f the bistable devices BS to 'BS Due to this the istabie'device BS isbrought back into its initial condiion -so that its 1output is deactivated triggering the nonostable device M5 to its unstable condition. Thus, is each bistable device is reset from the l-condition to he '0-conditionyacarry pulse is produced. By the trailng edge of the 6.8 s. pulse produced'at the output of hemonostable 'deviceMS the monostable device MS; s triggered to its unstable condition andby the negative L3 ,uS. pulse appearing at its O-outputthe output of the gate G is deactivated' so that the bistable device B5 s triggered into its 1-condition viathe OR-gate 'M At he end of'this" resetting operation the counter BS is :onsequently in'the '001'0 condition and hence registers he number 2. 'This tends to indicate that by resetting ill the bistable devices BS to their 0-conditions with :he help of the so called doubling pulse, the resultant Barry pulses will condition the counter to register a numaer having a value which is twice that of the previously itored number.

The second decimal digit 2 or 0010 in Aiken code if the decimal number 123 may now be fed to the coun- ;er. During the time interval t a pulse *isfedto the biitable device .BS via the gate G and the OR-gate M in this manner the bistable device B5 is triggered back into its O-condition and due .to this a carry pulse'is produced at its 'l-output setting the bistable device B8 to the 1-condition. After this operation only the'bistable device BS of the counter is in the l-condition and hence the number 4 is registered in the counter.

Afterwards a doubling pulse is again'applied to the bistable devices B5 and due to this the biitahle device BS is brought back into its 0-.cond ition producing a carry pulse at its l-output which'triggers the bistable BS into its l -condition. The positive pulse appearing at the l-output of this bistable device is not passed through the gate G since the input 2 of this gate is deactivated but the negative step appearing at the O-output of bistable device B5 triggers the monostable device M57 into its unstable condition. The trailing .edge of the pulse thus produced at the output of monostable device M8 triggers the monostable device M8 into its unstable condition due to which the bistable devices BS and B5 are triggered via the gates G and G respectively. Consequently,=after this operation the first, third and fourth stages ofthe counter are in-their l-conditions, Whereas the second stage isin its O-condition, so that the counter registers the number 13 or 8+5. The adding of 5 has been done for the following reason. After the doubling operation of the digit 4 the counter should be in the position i. e.3 steps away from the final or zero position of an 11' state counter. Since in fact a 16 state counter is used the counter isat that moment 8 steps away from theabove zero positio'n." Hence, to advance the counter to a position wherein it" is three steps away from the zero position'five countsmust be added. 7

The last decimal digit 3 or 0011 may now be registered.

During the time interval t the bistable device 38 is triggered to its l-condition via the gate G and the OR- gate'Mg. During the'time interval 1 the bistabledevice BS is triggered back to its O-condition via the gate Gg, producingacarry signal at its'1 output, which sets bistable device B8 back to its O-condition thus producing another carry pulse. In an analogousgmanner the bistable devices BS 'andBS are reset totheir 0co'ndition so that finally all the bistable devices BS 'to B3 of the counter four bistable devices to the four inputs of the coincidence gate G (FIG. 1) the output of which is connected to the winding of a relay (not shown) viaan amplifier. In this manner when all the bistable devices are in their O-conditions at the'end of a proof operation, it is clear that the output of G willbe'activated andconsequently that the not shownrelaywill be operated thus indicating that'the number fedto the calculating apparatus satisfies the proof condition.

Another particular example, namely the proving of the number 916 will now be described.

When the first digit 9 or 1111 is fed to the counter the following operations take place. During the -time interval t the bistable-device BS is triggered into its 1'-condition; during the time interval 7 the'bistable device B5 is triggered into its 1-condition;;during the time interval t the bistable device BS is brought back to its O-condition andhence produces a'carry pulse which triggers'the bistable device BS back to its O-condition. In this'manner the latter bistable device 'BS also produces a carry pulse which triggers the bistable device B8 into its 1 condition. "Finally during the time interval t the bistable device BS isset to 'its l-condition. As the bistable device B8 is brought intoits l-condition the monostable devices M8 and M8 are operated so that'a trigger pulse is applied via the OR-gate M and AND gates G and G to the bistable devices "BS and E8 respectively which are thus -set=to their 0 and l-coriditionsrespectively. Due to th'is the bistable device BS produces a carry pulse which brings the bistable BS in its -1-condition. At the end of this operation the counter registers the number 14=9+5 since the bistable devices B5 to B5 are in their l-condition whereas the bistable device BS is in its O-condition.

After-wards, when the monostable device M8 is triggered to its unstable condition at the start of the doubling operation the input 2 of AND gate G is activated and due to the bistable B5 being'in its l-condition the output of the gate G is activated. Also the trailingedge of the pulse appearing at the output of the monostable device M5 triggers the monostable device MS into its unstable condition which produces the so called doubling pulse. This pulse triggers the bistable devices BS 0 to B8 back to their O-conclitions so that a carry pulse appears at the l-outputs of the bistable devices B8 and E5 thus bringing the bistable devices B5 and B8 to the l-condition. In the-same manner as described above the bistable device B8 produces a carry pulse (on lead i) towards the stages BS and B8 which are set to theirl and 0 condition respectively. Due to ES being brought back to its O-condition a carry pulse is produced at its 1 output which triggers the bistable device B5 back to its O-condition.

At the end of this operation the counter registers the number 1. This is due to the fact that the carry digit of 5 which has been addd to the digit 9 has also been doubled by the doubling operation so that in fact 10 has been added'to the digit 9. Therefore 5 has tobe subtracted from this result or since mod 11 of the result has to be taken 6 has to be added. In this manner the counter will "register 1+6 or'7 which is right since (9X2) mod 11 7 dition for 18.

The negative trailing'edge of this 120 microsecond pulse triggers the nionostable device MS into its unstable condition' for 3.31nicroseconds and the leading edge of the pulse thus appearing at the O-output of monoare in their 0-condition and thus indicate that the number satisfies to the mod llv roof condition. This may also be physically indicated by connecting the O-o'ut'putof the stable device M8 triggers the monostable devices Bs andBS to the l-condition via the gates G and G respectively thus adding 6 to the previous result 1. I Indeed at the end of this operation the bistable de- 9 vices ES -B8 are in the l-condition whereas the bistable device B8 is in the O-condition, so that the counter registers the number 7 as required.

The next digits 1 and 6 of the number 916 may then be registered in the counter in an analogous manner to the one described above and at the end of this operation the bistable devices BS and E5 should all be in their O-condition since [(O+9) 2+1] 2+6=44 and 44 mod 11:0.

When the decimal digit or binary 0000 is applied to the calculating apparatus the input of the OR gate M is activated and due to this the number already registered in the counter will be multiplied by 2. I

It may be necessary to reset the calculating apparatus to the zero position e.g. when the number which has been fed to it does not satisfy the proof condition since the different bistables BS are then in arbitrary positions. In this case the monostable device M8 is triggered to its unstable condition for 2.2 milliseconds. Due to this the inputs 2 of AND-gate G and OR gates M and M are activated. Due to the input 2 of the gate G being activated B pulses are allowed to pass through this gate. They are applied on the one hand to the l-inputs of the bistable devices B8 which are thus reset to their 1- condition and on the other hand to the monostable device MS which is each time triggered to its unstable condition, thus bringing the bistable devices back in their O-condition. It is to be remarked that the triggering of the bistable device B8 remains without effect on the preceding bistable devices since the input leads 2 of the OR-gates M and M remain activated during the entire 2.2 millisecond duration of the pulse output of M8 When it is desired to make the proof by 13 instead of by 11 described below, it is clear that it is suffieient in this case to couple the output of the OR-gate M to the bistable devices B5,, and B5 instead of to BS and BS since 3 instead of 5 has to be added. Further the output of the OR-gate M must then be coupled to the inputs of the bistable devices B5 and B8 instead of to B8 and E8 since 10 must be added. Indeed, when 3 is doubled, 3 must afterwards be subtracted or since mod 13 of the result is taken, 10 must be added.

The above description discloses how the different bits of each decimal digit are fed to the calculating apparatus, and more especially to the four stage binary counter included therein in accordance to their weight, i.e. 2, 4, 2, 1 respectively, during the time intervals t t t and t allotted to each of these bits. Only afterwards is the multiplication, or doubling, operation executed. However by using a memory device 'to store the first digit during the time interval t this time interval may be used for execution of the multiplication operation. This introduces another particular advantage when the code used is the 2-4-2-1, code. Indeed,,in the first embodiment the first and thirdbits of each digit are fed to the binary stage of the counter having the weight 2, during the time intervals t and t respectively. Hence, when the first bin'ary bit is a 0 and when the third 'binary bit is a l the binary stage with'weight 2 is only triggered once. This is also the. case when the first binary bit is a l and when the third binarybit is a 0. However, when the first binary bit is a 1 and when simultaneously the third binary bit is also a 1 it is clear that the binary stage with weight 2 will be triggered twice. With the fact in mind that two triggerings of the binary stage with weight 2 corresponds to a single 3 triggering of the binary stage with weight 4, another embodiment of the calculating apparatus according to the invention has been designed wherein the first bit of each digit is stored during the time interval t in which the multiplication operation is executed, and the binary stage with weight .2 or 4 is triggered during the time interval t depending upon the value of the first and third bits. This embodiment will now be described in detail with reference to FIG- URE artists The calculating apparatus shown therein includes the four stage binary counter constituted by the bistable devices BS -BS each acting as a scale-of-two counter and each being triggered when a positive voltage step is applied thereto. The different time intervals t -t are allotted to the 4 binary bits of each digit fed to the calculating apparatus and the A pulses constitute sensing pulses. The different digits of the information to be proved are serially fed to the apparatus via theinput terminal IN while the above sensing or A pulses are applied to this apparatus via the terminal A.

The operation of the above calculating apparatus will become clear from the following; 7

When the first bit of a binary digit fed to the counter is a 0 the input 2 of the coincidence gate G is not activated. so that the bistable device BS remains in its 0 condition. However, when the first bit of the binary digit fed to the counter is a 1 the input lead 2 of the gate 6.; is activated and when an A pulse is applied to the input 1 of this gate during the time interval t i.e. when the input 3 of the gate G is activated, it is clear that this A pulse will be able to trigger the bistable device BS to its l-condition, thus deactivating the input lead 2 of the AND-gate G and activating the input leads 2 of the AND-gates G and G If the second bit of the digit fed to the calculating apparatus is a 1 the input 2 of the gate G is activated and when an A pulse is applied to the input 1 of this gate during the time interval t in which the input 3 of this gate G is also activated, the bistable device BS3 is triggered via the OR-gate M When the third bit of the binary digit fed to the calculating apparatus is a 0 the input leads 3 of the gates G and G are not activated, whereas the input 3 of the gate G is activated due to the connection of an inverter I between the input terminal IN and the input lead 3. When now the first bit of the digit is a 1; the input lead 2 of the gate G is activated, so that the output lead of gate G will be activated when an A pulse is applied to its input 4 during the time interval t in which its input 1 isactivated. Thus the bistable device BS with weight 2 will be triggered via the OR-gate M This corresponds to'what 'has been previously explained since if the first bit is a 1 while the third bit is a 0, the binary stage with weight 2 need only be triggered once. I

.Howeverif the third'bit of the digit fed to the calculating apparatus is a 1 the input 3 of the gate G will remain deactivated while the input leads 3 of the gates G and G will be activated; If the first bit of this digit is a O, the input leads 2 of-the'gates G and G are activated and deactivated respectively 'so'that, if a pulse is applied to the input leads 4 of these gates during the time interval t;; in which the input leads 1, of these gates are activated, only the output lead of t the gate G will become activated and hence will be able to trigger the bistable device BS via the OR-gate M This corresponds to what has been previously explained since ifthe first bit of a digit fed to the counter is a 0 while the third bit of this digit is a. 1 the binary stage with weight 2 included in the calculating apparatus need only be triggered once. However, if the first -bit0f the digit fed to the counter is a Ltheinput leads 2 of the gates G and G are respectively-deactivated and activated so that, if an A pulse is applied to the input leads 4 ofthese gatesdurin'grthe time interval t when the input leads lrof these gates are activated only. the output lead of the gate G; will be activated. In thismanner the bistable-device BS with weight 4 will be triggered via the OR-gate M This also corresponds to what has been previously explained'since if the first andthird binary bits of the digit fed to the counter are both 1 the binary stage of weight 4 must be triggered.

The fourth bit of a digit'fed to the calculating apparatus is only able to trigger the bistable device BS if it is a 1. Indeed, only in this case is the input lead 2 of the gate G activated so that also only in this case can the output lead of this gate G become activated by an A pulse applied to the input lead 3 during the time interval L; in which theinput lead'l of this gate G is activated.

As already mentioned above the time interval 1 is used for executing the doubling operation and therefore the gate G has been provided. Since the input leads land 2 of this gate are respectively connected to the input terminal A-and-to the terminal which is activated during the time interval t it is clear that during this time interval t a number of 'A pulses may be fed to the O-inputs of the bistable devices BS BS in order-to-reset them to their O-conditions, thus executing the multiplication operation.

It is alsotobe. remarked'that when starting a calculating operation with all the bistable'devices in their O-condition, the counter is in the position corresponding to the decimal number 11 at theend of the operation if the number-fed to the calculating apparatus satisfies to the 11 proof. This means that the bistable devices'BS BS andBS are then in-their, l-condition whereas the bistable deviceBS is in its O-condition. For detecting the ll-position the outputs 1 of the bistable devicesBS BS and B5,, have therefore been connected to the input leads-1, 2 and-4 of a gate G whereas the O-output of the bistable deviceBS is connected to the input lead 3 ofthe abovegate G This counter hasonly been very schematically represented but it should be remarked that, contrary to the counter BS used in the first embodiment, the counter B5 only delivers a carry pulse'representativeof 5 input counts, towards the stages BS; and BS .whenit reaches its 16th position i-.e. after-the'last stage BS has-been triggered back into its 0-condition. This simplifies the counter since a correction carry of 6 such as is required in the first embodiment is never necessary.

It should further also be remarked that althoughthe counter isbrought toits position 11 after an ll-proof it need not necessarily be brought back to its zero position before starting another'll proof.

\Vhile the principles of the invention have been described above in connection with specific apparatus, it is to beclearly understood-that this description is made only by Way of example and not as a limitation on the scope of the invention, as-set forth in the objects thereof and in the following claims. e

We claim: v

1.-In apparatus for calculating a linear digital=functi0n of the various decimal digits a; which form a decimal number, for the purpose of verifying a manifestation of said number, the combination of:

a binary counter, means for sequentially manifestating each digit of a set of decimal digits in a four bit-binary code, means coupled to said manifesting means for applying said manifested digits to said counter with the binary bits thereof individually added into bistable'stages of corresponding weight in said counter, and means coupled tosaid counter for doubling the contents thereof, after each said application of a manifested digit, by resetting all of the bistable stages therein to a predetermined condition and by applying carry signals resulting from said'resetting to given stages of said counter,

] wherebyeach partial sum resulting from the application of a manifested; decimal digit to the said'counter is multiplied by the'factor' '2, ,and thus whereby succes sive manifestations of decimal digits are in effect multiplied by-successive powers of the factor 2 and summed. i

' 2. Calculating apparatusaccording to claim 1 wherein said: counter comprises: e v

four bistable"deviceshaving the weights 2, 2 2 and 2 'respectivelyinterconnected to form a p-state device where p is a prime integer between 8 and 15, one output of the fourth bistable device being so connected to inputs of certain of the other bistable devices that when said one outputis activated the states of the said certain bistabledevices arereversed,

first gating means having one input coupled to the other output of said fourth bistable device, and having another input controlled by said doubling means, and having an output coupled to said certain bistable devices,

so that if said other output of said fourth bistable device is. activated during operation of said doubling means the states of said certain devices are reversed.

3. Calculating apparatus according to claim 1 wherein said counter comprises:

fourbistable devices-having thewcights 2, 2 2 and 2 respectivelyinterconnected to form a p-state device, where p is aprimeinteger between 8 and 15, oneoutput of the fourth bistable device being so connected' to inputs of certain of the other bistable devices that whensaid one output of said fourth device is activated the states of said certain devices are reversed.

4. Calculating apparatus according to claim 3, wherein said applying means includes:

a timing arrangement for sequentially controlling the said additions of said four binary bits of eachsaid decimal digit. manifestation, in four distinct time intervals, t t t and respectively; and wherein said doubling means vincludes:

meansoperative after the .applicationof said four binary bits of each said manifestation to apply a resetting pulse to the O-inputs of each of said four bistable devices of said counter.

5. Calculating apparatus as claimed in claim 3 wherein:

each said decimal digit is manifested in the 2421 binary code, e.g. the Aiken code, and wherein said apparatus includes:

a fifth bistable device, serving as a memory device, a timing arrangement for controlling said applyingmeans during four distinct time intervals t to so that the first binary bit of each. said decimal digit is fed by said feeding means to said fifth bistable device, during time interval 1 Whereas the second and fourth-bits of said decimal digit are fed to said third and first bistable fdevic'es during time intervals t and t respectively, second gating means conditioned by the 'O-output of said fifth bistable device andfby said timing arrangement so that if the first binary bit is a0 the third bit-isfed, during the time interval t to said second bistable device, and fourth gating means conditioned by the l-output of said fifth bistable device and by said timing arrangement, so that if the first bit is a 1 the third bit is fed during the time interval 1 to said secondor-third bi'sable devices depending upon whether said third bit'isa 0 or a 1, respectively; and wherein said doubling means includes:

means operativeduring the time interval ti to apply a'resetting pulse'to all of the 0 inputs of said four bistable'devices of said counter in order to reset them to their 0 conditions.

References Cited in the file of this patent UNITED STATES PATENTS 3,017,091 Ulrich Jan. 16, 1962 Rouche :Nov. 3, 1959. 

1. IN APPARATUS FOR CALCULATING A LINEAR DIGITAL FUNCTION OF THE VARIOUS DECIMAL DIGITS A WHICH FORM AI WHICH FORM A DECIMAL NUMBER, FOR THE PURPOSE OF VERIFYING A MANIFESTATION OF SAID NUMBER, THE COMBINATION OF: A BINARY COUNTER, MEANS FOR SEQUENTIALLY MANIFESTATING EACH DIGIT OF A SET OF DECIMAL DIGITS IN A FOUR BIT BINARY CODE, MEANS COUPLED TO SAID MANIFESTING MEANS FOR APPLYING SAID MANIFESTED DIGITS TO SAID COUNTER WITH THE BINARY BITS THEREOF INDIVIDUALLY ADDED INTO BISTABLE STAGES OF CORRESPONDING WEIGHT IN SAID COUNTER, AND MEANS COUPLED TO SAID COUNTER FOR DOUBLING THE CONTENTS THEREOF, AFTER EACH SAID APPLICATION OF A MANIFESTED DIGIT, BY RESETTING ALL OF THE BISTABLE STAGES THEREIN TO A PREDETERMINED CONDITION AND BY APPLYING CARRY SIGNALS RESULTING FROM SAID RESETTING TO GIVEN STAGES OF SAID COUNTER, WHEREBY EACH PARTIAL SUM RESULTING FROM THE APPLICATION OF A MANIFESTED DECIMAL DIGIT TO THE SAID COUNTER IS MULTIPLIED BY THE FACTOR 2, AND THUS WHEREBY SUCCESSIVE MANIFESTATIONS OF DECIMAL DIGITS ARE IN EFFECT MULTIPLIED BY SUCCESSIVE POWERS OF THE FACTOR 2 AND SUMMED. 